Quantum simulations of time-dependent Hamiltonians beyond the quasi-static approximation

TL;DR

This paper introduces a non-perturbative method using flow equations and Fourier expansion for simulating time-dependent quantum systems, surpassing the limitations of quasi-static approximations.

Contribution

It presents a novel approach that enables accurate quantum simulations of time-dependent Hamiltonians beyond perturbative and adiabatic regimes.

Findings

Successfully simulates Lambda-system dynamics beyond adiabatic approximation

Demonstrates quench in a Chern insulator during a quantum phase transition

Shows potential for more accurate quantum simulations of complex time-dependent systems

Abstract

Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with an approach based on flow equations and a multi-mode Fourier expansion. The potential of the quantum simulations that can be achieved with our approach is demonstrated with the pedagogical example of a Lambda-system and the quench in finite time through a quantum phase transition of a Chern insulator in a driven non-interacting Hubbard system. The example of the Lambda-system demonstrates the ability of our approach to describe situations beyond the validity of adiabatic approximations.